Convex grating types for concentric imaging spectrometers

The properties of convex gratings fabricated by electron-beam lithography are investigated. Three grating types are shown. The first is a single-panel, true blazed grating in which the blaze angle stays constant relative to the local surface normal. This grating provides high peak efficiencies of approximately 88% in the first order and 85% in the second order. The second grating has two concentric panels, with each panel blazed at a different angle. This type permits flexibility in matching the grating response to a desired form. The third type has a groove shape that departs from the sawtooth blazed profile to increase the second-order bandwidth. All these types are difficult or impossible to produce with conventional techniques. The gratings compare favorably with conventional (holographic and ruled) types in terms of efficiency and scatter. Simple scalar models are shown to predict the wavelength response accurately. These gratings allow the optical designer to realize fully the considerable advantages of concentric spectrometer forms.     

Replication of a holographic ion-etched spherical blazed grating for use at extreme-ultraviolet wavelengths: topography

We have measured the topography of a holographic ion-etched spherical blazed grating and three of its replicas using an atomic force microscope. The master grating had a roughness of less than 5 angstroms rms, a blaze angle of 2.5 degrees, and an antiblaze angle of 3.3 degrees. Thus the groove profile was more triangular than sawtooth. We find that the replication process did not significantly change the master grating. Moreover, we find no significant difference in roughness, blaze angle, or antiblaze angle between the master and its replicas before or after multilayer coating. However, bumps were observed on the gratings after coating, the cause of which is not understood. Although widespread, they occupy a relatively small fraction of the total area.     

Mo/Si multilayer-coated ruled blazed gratings for the soft-x-ray region

Two Mo/Si multilayer-coated blazed gratings have been fabricated for operation at soft-x-ray wavelengths above the Si L edge, λ ≥ 12.4 nm, at (near) normal incidence. The sawtooth profile of the grating structure was mechanically ruled into a 200-nm Au film that was deposited onto a plane glass substrate. To smooth the rough Au surface and to prevent interdiffusion of the Au film with the upper Mo/Si multilayer, a carbon film was evaporated onto the Au grating surface of one of the gratings before the deposition of the multilayer coating. We matched the multilayer grating, working on blaze in the third diffraction order, in which an absolute diffraction efficiency of 3.4% at a wavelength of 14 nm was measured, whereas only 1.1% was achieved for a similar grating (without a carbon interlayer). These efficiencies are higher than those obtained for other ruled blazed gratings reported in the literature. As a result of the multilayer and grating periodicity, the wavelength of diffraction can be tuned bya rotation of the grating, which is important for application in a soft-x-ray monochromator.     

Performance of normal-incidence molybdenum-yttrium multilayer-coated diffraction grating at a wavelength of 9 nm

The first experimental investigation of a normal-incidence Mo-Y multilayer-coated diffraction grating operating at a 9-nm wavelength is reported. The substrate is a replica of a concave holographic ion-etched blazed grating with 2,400 grooves/mm and a 2-m radius of curvature. The measured peak efficiency in the -3 order is 2.7% at a wavelength of 8.79 nm. To our knowledge, this is the highest normal-incidence grating efficiency ever obtained in this wavelength region.     

Scanning methods for production of blazed relief gratings

Abstract

New methods for the production of blazed relief grating profiles using grating masks with either binary or harmonic transmittance have been developed. These methods are based on the recording of a scanning wave, properly modulated by a mask, through a grating period into photoresist. The applicability of the gratings produced by this method would be especially in the infrared or near-infrared wavelength regions in the reflection mode. These methods have been theoretically analysed and the principal ideas of the methods were experimentally verified.     

Groove profile modification of blazed gratings by dip coating with hardenable liquids

We modify groove profile of various blazed gratings with groove densities as great as 3600 lines/mm by dip coating with hardenable liquids with the aim of reducing the blaze angle. The groove profiles resulting from coatings with different layer thickness are measured by atomic force microscopy. A highly reproducible blaze angle reduction to as high as a factor of 6 is achieved with mechanically ruled as well as ion-beam-etched holographic blazed gratings. Blaze angles, to as small as 0.7 deg, which are required for vacuum-UV and soft-x-ray applications but can hardly be formed with sufficient groove profile accuracy by direct ruling, are realized with this coating technique.     

Efficiency and long-term stability of a multilayer-coated, ion-etched blazed holographic grating in the 125-133-Å wavelength region

The efficiency of an ion-etched blazed holographic grating was measured by the use of synchrotron radiation in the 125-133-? wavelength range and at near-normal incidence. The grating had a Mo-Si multilayer interference coating that resulted in a peak normal-incidence efficiency of 13% in the second grating order and at a wavelength of 128 ?. This is the highest efficiency obtained to date from a multilayer-coated grating in this wavelength region and at normal incidence. These measurements are compared with similar measurements performed on the same grating 4.5 years later. Over this time the peak grating efficiency decreased from 13% to 8%, and this result is attributed to the decrease in the reflectance of the multilayer coating from 55% to 42%. Oxidation and contamination of the multilayer with carbon appear to be the causes of these losses. The groove efficiency of the grating substrate in the second order is 23%.     

Polarization and efficiency of a concave multilayer grating in the 135-250-Å region and in normal-incidence and SeyaNamioka mounts

A molybdenum/silicon multilayer coating was applied to a holographic ion-etched blazed grating substrate that had 2400 grooves/mm and a radius of curvature of 2.2 m. Scanning probe microscopy yielded the same surface microroughness (5 ? rms) before and after deposition of the multilayer. The efficiency and polarization performance of the grating was measured by synchrotron radiation in the 135-250-? wavelength region. In the second grating order and the second Bragg order of the multilayer coating, the peak normal-incidence efficiency was 7.5% at a wavelength of 147 ?, representing a groove efficiency of 27%. At an angle of incidence of 35°, the polarization performance of the grating was 95%-100% in the 210-250-? wavelength region. In a Seya-Namioka spectrometer mount at an angle of incidence of 30°-40°, the grating is a nearly perfect polarizing optical element in the wavelength bands between 125 and 300 ?, which are covered by the multilayer coating.     

Fabrication of holographic blazed grating with Fourier synthesis exposure

A simple, direct, and universal fabrication method for holographic blazed gratings is proposed and a 79 lines/mm holographic echelle grating with 4 μm depth quasi-triangular grooves experimentally demonstrated as an example of a blazed grating fabricated directly by Fourier synthesis exposure. With the method, we converted a periodic grating groove profile into the exposure energy spatial distribution on the surface of a photoresist with the response characteristics of the particular photoresist. Then the exposure energy could be decomposed into a series of sinusoidal functions using Fourier series, and realized by superposing a series of two-beam interference patterns. In contrast with mechanically ruled gratings, the fabrication process of holographic gratings is quite quick and low cost, and especially no Rowland ghosts appear in their dispersion spectrum. The reported work will offer a new approach for blazed grating fabrication with a holographic process.     

High-efficiency MoRu-Be multilayer-coated gratings operating near normal incidence in the 11.1-12.0-nm wavelength range

MoRu-Be multilayer coatings were applied to two diffraction gratings for the purpose of enhancing their normal-incidence efficiency in the 11.1-12.0-nm wavelength range. The grating substrates were replicas of a holographic master grating that had a blazed groove profile with 2400 grooves/mm and a 2-m radius of curvature. The relatively low average microroughness (0.8 nm) of the grating surfaces contributed to the relatively high groove efficiency of the grating substrates and the reflectance of the MoRu-Be multilayer coatings. The peak efficiency, measured with synchrotron radiation, was 10.4% in the second diffraction order at a wavelength of 11.37 nm.     

利用光栅闪耀特性优化低通滤波器

为了滤除有效光信号中的光噪声,本文提出了一种利用光栅的闪耀特性将噪声和有效信号之间的夹角角度差放大,再通过光阑得到有效光信号的方法。通过分析和仿真,使用光栅的1、2级闪耀对入射时微小角度差进行放大比较适宜。放大倍数会随着闪耀光栅的周期的减小而增大。负斜入射角度差的放大效果比正斜入射的效果更好。     

Design of transmission blazed binary gratings for optical limiting with the form-birefringence theory

The structure of transmission blazed binary gratings for optical limiting is designed with the form-birefringence theory. This kind of grating has subwavelength features, can imitate the transmission blazed grating effectively, and has higher efficiencies than a transmission blazed grating with a subwavelength structure. The diffraction efficiencies are calculated and analyzed. For the normal incident light with 10.6 microm wavelength, the transmissivities for the designed grating at 0 degrees deviation angle for TE and TM polarizations are 0.05% and 5.09%, respectively, which are basically identical to the results of the finite-difference time-domain method. The diffraction efficiencies of the first transmitted order for TE and TM polarizations are 93.95% and 83.88%, respectively.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

Near-normal-incidence extreme-ultraviolet efficiency of a flat crystalline anisotropically etched blazed grating

We have measured the extreme-ultraviolet (EUV) efficiency at an angle of incidence of 10 degrees of a flat crystalline anisotropically etched blazed grating. The measured efficiencies are high for uncoated gratings and agree well with a calculated model derived from a reasonable estimate of the groove profile. The highest groove efficiencies derived from the measurements are 48.8% at 19.07 nm and 64.1% at 16.53 nm for the -2 and -3 orders, respectively, which are comparable to the best values obtained yet from a holographic ion-etched blazed grating. This presents opportunities to instrument designs for high-resolution EUV spectroscopy in astrophysics where high efficiency in high orders is desirable.     

Analytic steady-state solutions to dynamic grating envelope

Abstract

The photorefractive holographic recording is a dynamic grating formulation process, where the grating is induced by the interference modulation of two beams, and the energies of the beams are exchanged with each other owing to their interaction in the induced grating. The grating modulation envelope is a comprehensive analysis for holographic dynamic recording and non-destructive readout, but analytic solutions can only be obtained by simultaneously solving the materials equations and the coupled wave equations. In this paper, based on Kukhtarev's model and Moharam's field function exact steady-state analytic expressions for dynamic grating envelopes are deduced for any constant values of light modulation depth and light excitation efficiency. Thus their approximations for straight formulation instead of parametric formulation are then obtained. These steady-state analytic solutions to envelopes describe the dynamic holographic recording and readout more clearly and exactly.     

Investigation of grating recording in betacarotene-polystyrene film

Abstract

An experimental study of grating recording in polymeric beta-carotene film is reported. Betacarotene was dissolved in a polystyrene host matrix and irradiated with a cw Ar laser. The formation of a holographic grating is demonstrated and the results of the grating stability measurements are presented.     

光刻胶灰化用于全息离子束刻蚀光栅制作

针对全息离子束刻蚀衍射光栅制作中,光刻胶光栅浮雕图形的制作是至关重要和困难的,引入O2反应离子刻蚀对光刻胶光栅进行灰化处理,给出光刻胶灰化技术在全息离子束刻蚀衍射光栅制作闪耀光栅、浅槽矩形位相光栅、自支撑透射光栅中的具体应用。实验结果表明,这一新工艺的突出优点是降低了苛刻的全息曝光、显影要求,使得光栅线条光滑、线空比和槽深可控。     

Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth

Abstract

Recording of holographic volume diffraction gratings in Du Pont's photopolymer HRS-150 is studied theoretically and experimentally. Particular attention is paid to the dynamics of the recording process. The temporal evolution of holographic gratings is monitored for a range of illumination intensities in two ways: (i) by means of a multiple-exposure approach when intensity profiles of recording beams are uniform, many holographic exposures are necessary and each exposure is carried out for a particular value of the total illumination intensity; (ii) by means of a single-exposure approach when intensity profiles of recording beams are strongly Gaussian and a volume grating with spatially distributed diffraction efficiency arises, depending on a local (average) value of the total illumination intensity. The second approach proves to be a useful tool providing us very quickly with qualitative information about the dynamics of the recording process while the first one, which is much more time-consuming, is more reliable for quantitative evaluations. The grating evolution is analysed theoretically by means of the well known photopolymerization-diffusion model. Discrepancies are found between the model and experimental results for low illumination intensities while qualitative agreement is found for higher intensities. For a given grating period, the discrepancies are interpreted in terms of insufficient change of the refractive index due to photopolymerization for low illumination intensities.     

Metal Gratings with Dielectric Coating of Variable Thickness within a Period

Abstract

The rigorous theory of diffraction is applied to metallic gratings with dielectric coating. The modulation depth of the profile between coating and air is assumed to be lower than the modulation depth of the profile between metal and coating. We call this levelling. For monochromator mounting together with a special coating thickness levelled single-coated gratings with blaze show a marked increase of the efficiencies for wavelengths greater than the blaze maximum wavelength. Optimal improvements run over two octaves of the wavelength.     

The generation of phase singularities at millimetre wavelengths by the use of a blazed grating

Abstract

A specially configured reflection blazed grating has been designed for operation at millimetre wavelengths to enable the efficient conversion of an incident plane wave into a beam with a phase singularity.